This article was originally published in the July/August 1999 issue of Home Energy Magazine. Some formatting inconsistencies may be evident in older archive content.

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Home Energy Magazine Online July/August 1999

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Calculating Water Heater Energy Use

Have you ever wanted to calculate how much energy a water heater would use annually in a given household? To make this task easier, Lawrence Berkeley National Laboratory (LBNL) has developed a straightforward equation that produces results close to those of simulation programs--without their baffling complexity.

The calculation is called Water Heater Analysis Model (WHAM). Its author, Jim Lutz, developed WHAM because he needed a quick way to model the potential effects of changes in water heater efficiency standards on the thousands of homes in the DOE/EPA Residential Energy Consumption Survey (RECS). This survey is a detailed collection of data on energy use in about 7,000 households that is done every three or four years by the Energy Information Administration. Lutz says that other people will benefit from the equation, too--anyone who needs to predict changes in a household's annual energy consumption caused by using different water heaters. This could include home energy raters, people in conservation programs, energy utilities, or even the writers of correlation-based energy analysis programs. Lutz warns that this equation is not for sizing water heaters--it doesn't tell you whether a given appliance will have the power and volume to cover a peak load. Nor should it be used to predict short-term energy use; it is valid only when use is averaged out over a period of at least a month.

A Better Option
Before WHAM, the only way to calculate a water heater's annual energy use accurately was to use the utility industry-developed simulation programs: TANK for gas water heaters and WATSIM for electric ones. These programs give extremely detailed models of an appliance's internal thermodynamics, and they have been validated and calibrated against real-life water heaters. Unfortunately, they require such arcane inputs as the emissivity of the tank cladding and the density of tank insulation. And they require lots of calculation time.

For convenience, most policymakers and utility conservation staff have chosen to make rough guesses at annual energy consumption based on the water heater's EF. But for households that use little hot water, the actual EF varies from simulation programs by as much as a factor of ten. WHAM, on the other hand, tracks very closely with both TANK and WATSIM over a wide range of hot-water consumptions, from 3 to 150 gallons per day.

Getting Results
WHAM requires the user to input seven variables about the water heater, its operating conditions, and its average daily draw. They are (1) the water heater's recovery efficiency (re); (2) its rated input power (Pon); (3) its standby heat loss coefficient (UA); (4) the water heater thermostat setpoint; (5) the inlet water temperature; (6) the air temperature outside the water heater; and (7) the volume of water drawn per day. The only variable that might not be easily obtained from the residents of the house or the label on the water heater is UA. However, Lutz says, it is possible to derive UA from the EF, re, and Pon, using the equation shown in Figure 1. Once collected, the variables are run through a straightforward formula to determine total water heater energy consumption (see Figure 2).

Of course, any simplified calculation needs to make assumptions. WHAM assumes that certain variables will be constant: the water and air temperatures; the specific heat and density of the water; and the water heater's re, Pon, and UA. Further, it assumes that all the water in the tank is always at the thermostat setpoint. However, to a first level of approximation, these assumptions are valid, as shown by comparing WHAM with the results of detailed simulation models that don't make these assumptions. For a quick, easy, and fairly accurate calculation of water heater energy consumption, WHAM is the way to go.

Figure 1. A water heater's standby loss coefficient, if not available from the manufacturer or the residents, can be determined with this calculation.*This figure refers to the temperature difference between the water in the tank and the air surrounding the tank during the test procedure.ÝThis is the length of the test procedure in hours.ýThis is the energy content of the water drawn from the heater during the 24-hour test.